Dons defender Andrew Considine handed the initiative to Neil Lennon's side in the 18th minute when he was sent off by referee William Collum for fouling Gary Hooper in the box although Jamie Langfield saved Anthony Stokes' penalty.
The Pittodrie men held out until the break but the numerical disadvantage took its toll in the second half as goals from Charlie Mulgrew, Joe Ledley, Kris Commons, with a spot kick, and Shaun Maloney, sealed a comfortable and expected win for the Parkhead side.
The Hoops' showpiece game against Motherwell at the national stadium on May 21 will be the first time the two clubs have met in the Scottish Cup final for 60 years and Celtic will be as strongly fancied then as they were against the Dons, whose form against them this season has been dismal.
Aberdeen went in to the game having lost 17 goals to the Hoops in four previous games this term, including a 4-1 defeat in the semi-final of the Co-operative Insurance Cup at the end of January.
Lennon had brought back Stokes and Gary Hooper after leaving them out against St Johnstone in midweek but the former had a wretched first half, wasting two good chances before the penalty miss.
In the fifth minute a wonderful Commons cross from the left was met by Stokes but the former Sunderland striker glanced his header wide of the far post.
Stokes had an equally good chance in the 13th minute when a long Mark Wilson free-kick saw him race past a sleeping Dons defence but his drive from 12 yards was blocked by Langfield at the expense of a corner, which came to nothing.
However, in the 18th minute, after Considine had been sent off for tripping Hooper in the box after he ran onto a Scott Brown pass, Stokes squandered an even better opportunity from the spot.
The Irishman drove his penalty to Langfield's right but the former Dundee keeper got down to block before Aberdeen skipper Zander Diamond forced the rebound behind for a corner which, again, the Dons survived.
Coincidentally, Langfield had saved a Stokes penalty after Considine had been sent off in the second minute when the two sides met at Pittodrie in the Clydesdale Bank Premier League at the start of February.
Langfield was proving to be Stokes' nemesis. The keeper saved again from the Celtic striker after he finished off a breakaway by firing in from the edge of the box.
The Granite City men were primarily concerned with their defensive duties but had their first chance in the 27th minute when Rob Milsom's floated cross found Chris Maguire 14 yards out but his header lacked the power to trouble Fraser Forster.
The rest of the first 45 minutes saw Celtic struggle to get past a solid red rearguard.
And it looked like being a long second half for the Dons as Langfield again had to come to the rescue less than two minutes after the restart.
Stokes and Hooper combined brilliantly at the edge of the Aberdeen box but the Englishman's close-range shot was blocked by the Dons keeper.
However, all Langfield's good work was undone in the 49th minute. He looked at fault when Celtic took the lead through Mulgrew.
After Milsom was booked for a foul on Beram Kayal 35 yards out, the former Dons defender knocked the free-kick into the box and it evaded everyone and caught Langfield off guard as it sped in at the far post.
In the 56th minute Maguire had the ball in the Celtic net but was ruled offside and a minute later Celtic confirmed their final appearance when Ledley latched onto a Stokes cross to send a shot from 12 yards past Langfield and into the corner of the net.
Aberdeen were down and out. In the 62nd minute defender Derek Young conceded a penalty when he brought down Stokes almost on the byline and this time Commons sent Langfield the wrong way from the spot.
The former Derby player then clipped the ball over the bar from just six yards after being set up by Stokes.
Then, Langfield saved at the feet of Hooper who had been sent clear with a clever pass from Celtic substitute Maloney, who had replaced Ledley.
But as Aberdeen tried to stem the tide, Maloney got himself on the scoresheet in the 83rd minute he converted a Wilson pass from almost on the goal-line and the Dons' misery was complete.